1
New Number: 4.52 | AESZ: 258 | Superseeker: 480 4215904 | Hash: bfb9f01124fd9980817cbf1b50f789c3
Degree: 4
\(\theta^4-2^{4} x\left(16\theta^4+224\theta^3+156\theta^2+44\theta+5\right)-2^{14} x^{2}\left(48\theta^4+48\theta^3-120\theta^2-66\theta-11\right)-2^{22} x^{3}\left(16\theta^4-192\theta^3-156\theta^2-48\theta-5\right)+2^{32} x^{4}\left((2\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 80, 24336, 11398400, 6632189200, ... --> OEIS Normalized instanton numbers (n0=1): 480, -16536, 4215904, -242723592, 151800032928, ... ; Common denominator:...
\((1024z-1)(256z-1)(1+512z)^2\)
| \(-\frac{ 1}{ 512}\) | \(0\) | \(\frac{ 1}{ 1024}\) | \(\frac{ 1}{ 256}\) | \(\infty\) |
|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(0\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) |
| \(3\) | \(0\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) |
| \(4\) | \(0\) | \(2\) | \(2\) | \(\frac{ 1}{ 2}\) |
2
New Number: 5.48 | AESZ: 247 | Superseeker: 608 22293216 | Hash: 6c0503129f3500c26cf001c1908a17f7
Degree: 5
\(\theta^4+2^{4} x\left(144\theta^4-192\theta^3-132\theta^2-36\theta-5\right)+2^{13} x^{2}\left(112\theta^4-512\theta^3+98\theta^2+50\theta+13\right)-2^{20} x^{3}\left(544\theta^4+384\theta^3+332\theta^2+108\theta+21\right)-2^{30} 5 x^{4}\left(12\theta^4-23\theta^2-23\theta-7\right)+2^{40} 5^{2} x^{5}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 80, 11024, 1850624, 343952656, ... --> OEIS Normalized instanton numbers (n0=1): 608, -85544, 22293216, -7629059800, 3042437418016, ... ; Common denominator:...
\((1+256z)(1280z+1)^2(256z-1)^2\)
| \(-\frac{ 1}{ 256}\) | \(-\frac{ 1}{ 1280}\) | \(0\) | \(\frac{ 1}{ 256}\) | \(\infty\) |
|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(0\) | \(\frac{ 1}{ 2}\) | \(1\) |
| \(1\) | \(3\) | \(0\) | \(\frac{ 1}{ 2}\) | \(1\) |
| \(2\) | \(4\) | \(0\) | \(1\) | \(1\) |
3
New Number: 14.7 | AESZ: | Superseeker: 48 3184 | Hash: 9e304ff532f3cfafc29dfac77fdff067
Degree: 14
\(\theta^4-2^{4} x\left(35\theta^4+50\theta^3+49\theta^2+24\theta+5\right)+2^{9} x^{2}\left(255\theta^4+722\theta^3+1027\theta^2+740\theta+227\right)-2^{14} x^{3}\left(1033\theta^4+4298\theta^3+7994\theta^2+7243\theta+2695\right)+2^{19} x^{4}\left(2699\theta^4+13730\theta^3+30984\theta^2+33699\theta+14443\right)-2^{24} x^{5}\left(5407\theta^4+26718\theta^3+63946\theta^2+80619\theta+38786\right)+2^{29} x^{6}\left(10081\theta^4+39658\theta^3+68604\theta^2+85851\theta+43438\right)-2^{34} x^{7}\left(17583\theta^4+63666\theta^3+51252\theta^2-1045\theta-18966\right)+2^{39} x^{8}\left(25019\theta^4+98594\theta^3+101972\theta^2-44371\theta-87630\right)-2^{44} x^{9}\left(29162\theta^4+103060\theta^3+189337\theta^2+75677\theta-39871\right)+2^{49} x^{10}\left(32428\theta^4+78424\theta^3+166293\theta^2+155877\theta+49943\right)-2^{54} x^{11}\left(33248\theta^4+85104\theta^3+119906\theta^2+105882\theta+49279\right)+2^{59} x^{12}\left(24144\theta^4+97280\theta^3+159468\theta^2+125460\theta+41819\right)-2^{67} 5 x^{13}\left(244\theta^4+1456\theta^3+3353\theta^2+3523\theta+1423\right)+2^{75} 5^{2} x^{14}\left((\theta+2)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 80, 5776, 422144, 32579856, ... --> OEIS Normalized instanton numbers (n0=1): 48, 46, 3184, 409910, -3351792, ... ; Common denominator:...
\((16z-1)(32z-1)(4096z^2-192z+1)(163840z^3+1024z^2+32z-1)^2(64z-1)^4\)
| ≈\(-0.009802-0.019I\) | ≈\(-0.009802+0.019I\) | \(0\) | \(\frac{ 3}{ 128}-\frac{ 1}{ 128}\sqrt{ 5}\) | ≈\(0.013353\) | \(\frac{ 1}{ 64}\) | \(\frac{ 1}{ 32}\) | \(\frac{ 3}{ 128}+\frac{ 1}{ 128}\sqrt{ 5}\) | \(\frac{ 1}{ 16}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(-\frac{ 1}{ 2}\) | \(0\) | \(0\) | \(0\) | \(2\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(-\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(1\) | \(2\) |
| \(3\) | \(3\) | \(0\) | \(1\) | \(3\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(1\) | \(2\) |
| \(4\) | \(4\) | \(0\) | \(2\) | \(4\) | \(\frac{ 1}{ 2}\) | \(2\) | \(2\) | \(2\) | \(2\) |
4
New Number: 6.16 | AESZ: | Superseeker: 2272 434311008 | Hash: f30ffc268310c175e914066ee270f47b
Degree: 6
\(\theta^4+2^{4} x\left(448\theta^4-544\theta^3-332\theta^2-60\theta-5\right)+2^{12} x^{2}\left(2576\theta^4-8416\theta^3+2808\theta^2+668\theta+35\right)-2^{20} x^{3}\left(9088\theta^4+5568\theta^3+5392\theta^2+3180\theta+667\right)-2^{28} 3^{2} x^{4}(2\theta+1)(744\theta^3+940\theta^2+798\theta+167)+2^{38} 3^{3} 5 x^{5}(16\theta^2+40\theta+33)(\theta+1)^2+2^{48} 3^{3} 5^{2} x^{6}(\theta+1)^2(\theta+2)^2\)
Maple LaTexCoefficients of the holomorphic solution: 1, 80, 30480, 9850112, 4649741584, ... --> OEIS Normalized instanton numbers (n0=1): 2272, -719992, 434311008, -343376572072, 316225589496736, ... ; Common denominator:...
\((768z-1)(256z-1)(256z+1)^2(3840z+1)^2\)
| \(-\frac{ 1}{ 256}\) | \(-\frac{ 1}{ 3840}\) | \(0\) | \(\frac{ 1}{ 768}\) | \(\frac{ 1}{ 256}\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(\frac{ 1}{ 2}\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) |
| \(\frac{ 1}{ 2}\) | \(3\) | \(0\) | \(1\) | \(1\) | \(2\) |
| \(1\) | \(4\) | \(0\) | \(2\) | \(2\) | \(2\) |
5
New Number: 8.74 | AESZ: | Superseeker: 4 436 | Hash: a0fbd8561e58a032d489a1dabee1e026
Degree: 8
\(\theta^4-2^{2} x\theta(22\theta^3+14\theta^2+9\theta+2)+2^{4} x^{2}\left(109\theta^4-74\theta^3-293\theta^2-258\theta-80\right)+2^{8} x^{3}\left(39\theta^4+414\theta^3+674\theta^2+504\theta+144\right)-2^{10} x^{4}\left(405\theta^4+1170\theta^3+1321\theta^2+424\theta-104\right)-2^{14} x^{5}(\theta+1)(12\theta^3+558\theta^2+1495\theta+1255)+2^{16} x^{6}(\theta+1)(\theta+2)(467\theta^2+1593\theta+1540)-2^{20} 5 x^{7}(\theta+3)(\theta+2)(\theta+1)(\theta-40)-2^{22} 5^{2} 7 x^{8}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 80, 1536, 56592, ... --> OEIS Normalized instanton numbers (n0=1): 4, 71/2, 436, 6728, 127212, ... ; Common denominator:...
\(-(-1+56z)(20z-1)^2(8z-1)^2(8z+1)^3\)
| \(-\frac{ 1}{ 8}\) | \(0\) | \(\frac{ 1}{ 56}\) | \(\frac{ 1}{ 20}\) | \(\frac{ 1}{ 8}\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(0\) | \(0\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(2\) |
| \(-\frac{ 1}{ 4}\) | \(0\) | \(1\) | \(3\) | \(\frac{ 1}{ 2}\) | \(3\) |
| \(\frac{ 1}{ 4}\) | \(0\) | \(2\) | \(4\) | \(1\) | \(4\) |
6
New Number: 8.83 | AESZ: | Superseeker: 208 642704 | Hash: 7314ca8e48f991223dc4e1c8b4893b95
Degree: 8
\(\theta^4-2^{4} x\left(116\theta^4+160\theta^3+119\theta^2+39\theta+5\right)+2^{9} x^{2}\left(2096\theta^4+5600\theta^3+5694\theta^2+2366\theta+355\right)-2^{15} x^{3}\left(4232\theta^4+22416\theta^3+28566\theta^2+11646\theta+1745\right)-2^{21} x^{4}\left(20616\theta^4+8496\theta^3-69074\theta^2-48074\theta-9335\right)+2^{27} x^{5}\left(49408\theta^4+114208\theta^3-29684\theta^2-42372\theta-9585\right)+2^{34} x^{6}\left(46496\theta^4-21984\theta^3-28956\theta^2-5580\theta+375\right)-2^{41} 5 x^{7}(2\theta+1)^2(344\theta^2+416\theta+163)-2^{48} 5^{2} x^{8}(2\theta+1)^2(2\theta+3)^2\)
Maple LaTexCoefficients of the holomorphic solution: 1, 80, 23760, 9900800, 4805155600, ... --> OEIS Normalized instanton numbers (n0=1): 208, 3154, 642704, -4424361, 3864242160, ... ; Common denominator:...
\(-(16384z^2-768z+1)(4096z^2+704z-1)(128z+1)^2(320z-1)^2\)
| \(-\frac{ 11}{ 128}-\frac{ 5}{ 128}\sqrt{ 5}\) | \(-\frac{ 1}{ 128}\) | \(0\) | \(\frac{ 3}{ 128}-\frac{ 1}{ 64}\sqrt{ 2}\) | \(-\frac{ 11}{ 128}+\frac{ 5}{ 128}\sqrt{ 5}\) | \(\frac{ 1}{ 320}\) | \(\frac{ 3}{ 128}+\frac{ 1}{ 64}\sqrt{ 2}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(3\) | \(0\) | \(1\) | \(1\) | \(3\) | \(1\) | \(\frac{ 3}{ 2}\) |
| \(2\) | \(4\) | \(0\) | \(2\) | \(2\) | \(4\) | \(2\) | \(\frac{ 3}{ 2}\) |